TAILIEUCHUNG - Advances in Database Technology- P15

Tham khảo tài liệu 'advances in database technology- p15', công nghệ thông tin, cơ sở dữ liệu phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 682 K. Kailing et al. Fig. 5. Folding techniques for histograms The technique of Papadopoulos and Manolopoulos top and the modulo folding technique bottom . Theorem 2. For any two trees ti andt the L -distance of the leaf distance histograms is a lower bound of the degree-2 edit distance oft and t Proof. Analogously to the proof of theorem 1. Theorem 1 and 2 also allow us to use leaf distance histograms as a filter for the weighted edit and weighted degree-2 edit distance. This statement is justified by the following considerations. As shown above the Li-distance of two leaf distance histograms gives a lower bound for the insert and delete operations that are necessary to transform the two corresponding trees into each other. This fact also holds for weighted relabeling operations as weights do not have any influence on the necessary structural modifications. But even when insert delete operations are weighted our filter can be used as long as their exists a smallest possible weight wmin for an insert or delete operation. In this case the term is a lower bound for the weighted edit and degree-2 edit distance between the trees ti and 2- Since we assume metric properties as well as the symmetry of insertions and deletions for the distance the triangle inequality guarantees the existence of such a minimum weight. Otherwise any relabeling of a node would be performed cheaper by a deletion and a corresponding insertion operation. Moreover structural differences of objects would be reflected only weakly if structural changes are not weighted properly. Histogram folding. Another property of leaf distance histograms is that their size is unbounded as long as the height of the trees in the database is also unbounded. This problem arises for several feature vector types including the degree histograms presented in section . Papadopoulos and Manolopoulos 10 address this problem by folding the histograms into vectors with fixed dimension. This is done in a piecewise .

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